The effect of charge transfer fluctuation on superconductivity in high temperature superconductors

$High-T_c$ Cuprates have been studied quite often as an effective one band $t-J$ model that neglects charge fluctuation between oxygen $2p^6$ band and copper $3d^{10}$ band, and Zhang-Rice singlet is just a hole in the model. However, recent Scanning Tunneling Spectra(STS) measurement on underdoped Cuprate shows that charge transfer gap is only of order $1~2$ eV. This small gap necessitates a re-examination of the charge transfer fluctuation. Here we modify the t-J model by including charge transfer fluctuation allowing the formation of doubly occupied sites. For certain parameters it is similar with the t-J-U model. This model is studied via variational Monte Carlo method(VMC). Our result shows that this model can give a unified behavior of superconducting dome with different long rang hopping parameters. The anti-correlation between charge transfer gap and pairing is also confirmed. More interestingly the charge fluctuation is found to affect pairing order parameter in different ways in underdoped and overdoped regions.